-3/2x+7/1=2x+7

Solution for -3/2x+7/1=2x+7 equation:

-3/2x+7/1=2x+7

We move all terms to the left:

-3/2x+7/1-(2x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3/2x-(2x+7)=0

We get rid of parentheses

-3/2x-2x-7=0

We multiply all the terms by the denominator


-2x*2x-7*2x-3=0

Wy multiply elements

-4x^2-14x-3=0

a = -4; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·(-4)·(-3)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{37}}{2*-4}=\frac{14-2\sqrt{37}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{37}}{2*-4}=\frac{14+2\sqrt{37}}{-8}
$